diff --git a/demos/qiskit_patterns/2_qiskit_patterns.ipynb b/demos/qiskit_patterns/2_qiskit_patterns.ipynb
index b4a1085..09c36a1 100644
--- a/demos/qiskit_patterns/2_qiskit_patterns.ipynb
+++ b/demos/qiskit_patterns/2_qiskit_patterns.ipynb
@@ -7,8 +7,7 @@
"source": [
"# Scaling Quantum Optimization with Qiskit Patterns\n",
"\n",
- "In this how-to we will learn about Qiskit Patterns and quantum approximate optimization. Qiskit Patterns define a four-step process for running algorithms on a quantum computer:\n",
- "\n",
+ "In this how-to we will learn about Qiskit Patterns and quantum approximate optimization. A Qiskit Pattern is an intuitive, repeatable set of steps for implementing a quantum computing workflow: \n",
"\n",
"\n",
"\n",
@@ -48,7 +47,7 @@
"id": "74b92ba5-c48a-405c-9c4b-04e985a7afbc",
"metadata": {},
"source": [
- "Max-Cut is a hard to solve optimization problem with applications in clustering, network science, and statistical physics. The goal of this problem is to partition the nodes of a graph into to sets such that the number of edges traversed by this cut is maximum.\n",
+ "Max-Cut is a hard to solve optimization problem with applications in clustering, network science, and statistical physics. The goal of this problem is to partition the nodes of a graph into two sets such that the number of edges traversed by this cut is maximum.\n",
"\n",
""
]
@@ -171,7 +170,6 @@
"H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n",
"\\end{align}\n",
"\n",
- "
\n",
"First, a variable change, we convert the binary variables $x_i$ to variables $z_i\\in\\{-1, 1\\}$ by doing\n",
"\n",
"\\begin{align}\n",
@@ -195,10 +193,11 @@
"\\begin{align}\n",
"H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n",
"\\end{align}\n",
- "
\n",
"\n",
- "We refer to this Hamiltonian as the **cost function Hamiltonian**. It has the property that its gound state corresponds to the solution that **minimizes the cost function $f(x)$**.\n",
- "Therefore, to solve our optimization problem we now need to prepare the ground state of $H_C$ (or a state with a high overlap with it) on the quantum computer. Then, sampling from this state will, with a high probability, yield the solution to $min f(x)$."
+ "\n",
+ "We refer to this Hamiltonian as the cost function Hamiltonian. It has the property that its gound state corresponds to the solution that minimizes the cost function $f(x)$.\n",
+ "Therefore, to solve our optimization problem we now need to prepare the ground state of $H_C$ (or a state with a high overlap with it) on the quantum computer. Then, sampling from this state will, with a high probability, yield the solution to $min~f(x)$.\n",
+ "
"
]
},
{
@@ -1362,7 +1361,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.9.7"
+ "version": "3.10.0"
}
},
"nbformat": 4,
diff --git a/demos/qiskit_patterns/imgs/eagle-heron-0.png b/demos/qiskit_patterns/imgs/eagle-heron-0.png
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diff --git a/demos/qiskit_patterns/imgs/eagle-heron.png b/demos/qiskit_patterns/imgs/eagle-heron.png
index 646e729..7927f06 100644
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